1. We heard a piece of news.
  2. We heard a news.
  3. We heard a radio news.
    Are all correct?
    Please comment. Thanks.

‘News’ is not used with the indefinite article and so 2 and 3 are not possible.

2. We heard the news.
3. We heard the radio news.
4. We heard the piece of news of radio/TV.
Are the all correct?

I assume that the ‘of’ instead of ‘on’ in 4 is a typo, in which case, yes if you add a definite article after ‘on’ in that sentence.
… on the TV/radio.

Dear Beeesneees, we are taught that we use on the radio but on TV/on television (without the definite article) as an expression.
We use on the TV when we mean TV-set, don’t we?


In that particular case either is possible. It could refer to the TV set.

Did you see it on (the) TV last night?
and a number of other expressions.

If that is confusing (which it probably is) stick with what you are taught.